Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503305019 |
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| Summary: | This paper deals with an initial boundary value problem with an
integral condition for the two-dimensional diffusion equation.
Thanks to an appropriate transformation, the study of the given
problem is reduced to that of a one-dimensional problem.
Existence, uniqueness, and continuous dependence upon data of a
weak solution of this latter are proved by means of the Rothe
method. Besides, convergence and an error estimate for a
semidiscrete approximation are obtained. |
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| ISSN: | 1085-3375 1687-0409 |